Mathematical models of cell self-organization | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 19, Issue 1, June 2011, Page 52-56 PDF (362.22 K) | ||||
| DOI: 10.1016/j.joems.2011.09.005 | ||||
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| Author | ||||
| Benoıˆt Perthame | ||||
| Univ. P. et M. Curie and CNRS, UMR 7598, Laboratoire Jacques-Louis, Lions, BC187, 4, place Jussieu, F75252 Paris cedex 05, France | ||||
| Abstract | ||||
| Various classes of Partial Differential Equations have shown to be successful in describing the self-organization of bacterial colonies, a topic also sometimes called socio-biology. For instance parabolic systems are standard; the classical Patlak–Keller–Segel system and Mimura’s system are able to explain two elementary processes underlying qualitative behaviors of populations and complex patterns: oriented drift by chemoattraction and colony growth with local nutrient depletion. More recently nonlinear hyperbolic and kinetic models also have been used to describe the phenomena at a smaller scale. We explain here some motivations for ‘microscopic’ descriptions, the mathematical difficulties arising in their analysis and how kinetic models can help in understanding the unity of these descriptions. | ||||
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